Answer:
A)No; any two cross sections of a cylinder that lie on planes parallel to the bases of the cylinder are congruent.
Step-by-step explanation: I had to answer it in class and got it right
Answer:
a) OA = 1 unit
b) BC = 3 units
c) OD = 2 units
d) AC = 3√2 units
Step-by-step explanation:
Given function:
![f(x)=\dfrac{2}{x}-2](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B2%7D%7Bx%7D-2)
<h3><u>Part (a)</u></h3>
Point A is the x-intercept of the curve.
To find the <u>x-intercept</u> of the curve (when y = 0), set the function to zero and solve for x:
![\begin{aligned}f(x) & = 0\\\implies \dfrac{2}{x}-2 & = 0\\\dfrac{2}{x} & = 2\\2 & = 2x\\\implies x & = 1\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Df%28x%29%20%26%20%3D%200%5C%5C%5Cimplies%20%5Cdfrac%7B2%7D%7Bx%7D-2%20%26%20%3D%200%5C%5C%5Cdfrac%7B2%7D%7Bx%7D%20%26%20%3D%202%5C%5C2%20%26%20%3D%202x%5C%5C%5Cimplies%20x%20%26%20%3D%201%5Cend%7Baligned%7D)
Therefore, A (1, 0) and so OA = 1 unit.
<h3><u>Part (b)</u></h3>
If OB = 2 units then B (-2, 0). Therefore, the x-value of Point C is x = -2.
To find the y-value of Point C, substitute x = -2 into the function:
![\implies f(-2)=\dfrac{2}{-2}-2=-3](https://tex.z-dn.net/?f=%5Cimplies%20f%28-2%29%3D%5Cdfrac%7B2%7D%7B-2%7D-2%3D-3)
Therefore, C (-2, -3) and so BC = 3 units.
<h3><u>Part (c)</u></h3>
<u>Asymptote</u>: a line that the curve gets infinitely close to, but never touches.
The y-value of Point D is the horizontal asymptote of the function.
The function is undefined when x = 0 and therefore when y = -2.
Therefore, D (0, -2) and so OD = 2 units.
<h3><u>Part (d)</u></h3>
From parts (a) and (c):
To find the length of AC, use the distance between two points formula:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
![\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points.}](https://tex.z-dn.net/?f=%5Ctextsf%7Bwhere%20%7D%28x_1%2Cy_1%29%20%5Ctextsf%7B%20and%20%7D%28x_2%2Cy_2%29%5C%3A%5Ctextsf%7Bare%20the%20two%20points.%7D)
Therefore:
![\sf \implies AC=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20AC%3D%5Csqrt%7B%28x_C-x_A%29%5E2%2B%28y_C-y_A%29%5E2%7D)
![\sf \implies AC=\sqrt{(-2-1)^2+(-3-0)^2}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20AC%3D%5Csqrt%7B%28-2-1%29%5E2%2B%28-3-0%29%5E2%7D)
![\sf \implies AC=\sqrt{(-3)^2+(-3)^2}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20AC%3D%5Csqrt%7B%28-3%29%5E2%2B%28-3%29%5E2%7D)
![\sf \implies AC=\sqrt{9+9}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20AC%3D%5Csqrt%7B9%2B9%7D)
![\sf \implies AC=\sqrt{18}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20AC%3D%5Csqrt%7B18%7D)
![\sf \implies AC=\sqrt{9 \cdot 2}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20AC%3D%5Csqrt%7B9%20%5Ccdot%202%7D)
![\sf \implies AC=\sqrt{9}\sqrt{2}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20AC%3D%5Csqrt%7B9%7D%5Csqrt%7B2%7D)
![\sf \implies AC=3\sqrt{2}\:\:units](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20AC%3D3%5Csqrt%7B2%7D%5C%3A%5C%3Aunits)
The equation was plotted using geogebra online graphing tool.
A function is said to be linear if it is a straight line graph and it can be represented by the equation:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Given the equation:
3x + 5y = 18
Plotting the equation using geogebra online graphing tool, the graph is attached.
Find out more at: brainly.com/question/21835898
Answer:
16 feet
Step-by-step explanation: